Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 786 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1849 (b) 1609 (c) 1369 (d) 1859
2. 2.A bag has 7 red, 2 white and 3 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/12 (b) 5/7 (c) 5/12 (d) 1/3
3. 3.In a class of 47 children, 28 like cricket, 26 like football and 12 like both. How many like at least one of the two? (a) 47 (b) 30 (c) 54 (d) 42
4. 4.The mean of 5 numbers is 11. When the number 5 is added to them, what is the new mean? (a) 8 (b) 9 (c) 11 (d) 10
5. 5.The mean of 4 numbers is 33. When the number 23 is added to them, what is the new mean? (a) 28 (b) 31 (c) 32 (d) 33
6. 6.What is the 11th term of the AP 3, 10, 17, 24, …? (a) 73 (b) 70 (c) 77 (d) 80
7. 7.What is the distance between the points (3, 1) and (18, 9)? (a) 17 (b) 289 (c) 18 (d) 23
8. 8.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
9. 9.A bag has 5 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 16 (d) 6
10. 10.If a + b = 10 and ab = 21, what is a² + b²? (a) 58 (b) 142 (c) 100 (d) 79
11. 11.The mean of 8 numbers is 27. When the number 54 is added to them, what is the new mean? (a) 29 (b) 27 (c) 30 (d) 31
12. 12.What is the mode of 14, 7, 7, 20, 14, 14 and 1? (a) 7 (b) 1 (c) 14 (d) 20
13. 13.What is the midpoint of the line joining (2, 13) and (4, 3)? (a) (3, 8) (b) (8, 3) (c) (6, 16) (d) (1, 5)
14. 14.A drawer has lots of blue, red, yellow, white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 5 (c) 6 (d) 2
15. 15.A drawer has lots of red, white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 6 (c) 2 (d) 3
16. 16.If a + b = 18 and ab = 77, what is (a − b)²? (a) 4 (b) 170 (c) 324 (d) 16
17. 17.A bag has 4 red, 8 green and 9 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 8/21 (b) 1/3 (c) 8/13 (d) 13/21
18. 18.What is the distance between the points (2, 11) and (10, 5)? (a) 11 (b) 14 (c) 100 (d) 10
19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
20. 20.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 140° (c) 40° (d) 320°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 121° (c) 60° (d) 240°
22. 22.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 400 sq cm (d) 1000 sq cm
23. 23.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 268 (c) 295 (d) 294
24. 24.In a class of 31 children, 21 like tea, 10 like coffee and 4 like both. How many like only tea? (a) 4 (b) 21 (c) 17 (d) 6
25. 25.What is the mode of 1, 12, 15, 3, 12, 1 and 1? (a) 12 (b) 3 (c) 1 (d) 15
26. 26.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 12 (c) 36 (d) 108
27. 27.What is the mean of 20, 9, 2 and 5? (a) 9 (b) 8 (c) 12 (d) 10
28. 28.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 155° (d) 105°
29. 29.What is the sum of the roots of x² − 9x + 14 = 0? (a) 8 (b) 14 (c) 10 (d) 9
30. 30.A bag has 11 yellow balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 17 (b) 12 (c) 13 (d) 2
31. 31.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 130° (d) 155°
32. 32.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 91 (d) 78
33. 33.How many factors does 51 have? (a) 2 (b) 5 (c) 3 (d) 4
34. 34.What is the mode of 7, 6, 5, 7, 3, 6 and 7? (a) 5 (b) 3 (c) 7 (d) 6
35. 35.What is the mode of 4, 11, 11, 20, 12, 12 and 12? (a) 11 (b) 20 (c) 12 (d) 4
36. 36.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
37. 37.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 12 (d) 16
38. 38.The mean of 4 numbers is 40. When the number 60 is added to them, what is the new mean? (a) 45 (b) 50 (c) 40 (d) 44
39. 39.In a class of 22 children, 17 like tea, 7 like coffee and 4 like both. How many like at least one of the two? (a) 22 (b) 24 (c) 20 (d) 16
40. 40.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 15 (b) 66 (c) 60 (d) 120

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